Sébastien Durand, Pierre Legendre, and S. Kim Juniper. 2006. Sonar backscatter differentiation of dominant macrohabitat types in a hydrothermal vent field. Ecological Applications 16:1421–1435.

Appendix A. Table A1 shows the definitions of the VE variables along with the transformation details, Table A2 the transformation trials for the VI data, and Table A3 the variables retained by forward selection.

TABLE A1. Definitions, transformations, and skewness values of the VE variables (variables describing echo shapes).

   Notes: The VE variables used in our analyses were selected out of a larger set of 66 variables in such way as to minimize collinearity among the variables. Then, out of four transformations (none, log, sqrt, and double sqrt), the transformation producing the lowest skewness values was applied to each of these variables. For all rising, setting, and complete sections found in our backscatters, the areas under the curves and the time spent were calculated. The following area and time spent proportions were also calculated: E1 rise / E1 complete and E1 rise / E2 rise. The points and values of maximum intensity found in E1 and E2, in both the original and smoothed curves, and the point and value of minimum intensity found between these maxima were also described. Finally, the statistical moments, a 7-class histogram of E1 intensity values, and the distances in the x and y directions, between the centroids of the E1 rising and setting sections, were calculated.

TABLE A2. Transformation trials for the VI data table and subtables.

   Notes: The presented values are the means of all skewness values computed on all VI data tables after different sequences of transformations. The lowest (best) skewness value for each data subset is in bold. Illogical transformations were not calculated (—). In the first set of transformation, either no transformation (None) was applied, or the effect of high intensity outliers on the distribution was reduced through a square root (Sqrt), double square root (Double Sqrt), log (Log), or modified arsine transformation (Mod.Arcsine). This modified form used the table maximum as the denominator in the calculation of proportions, prior to computing the square root and then the arcsine, instead of the object’s maximum in the ordinary arcsine transformation (Sokal and Rohlf 1995). With this modification, all these transformations conserved both the strength and shape information found in backscatters. In a second step, on all the newly transformed tables, we performed either no transformation (None), an ordinary arcsine transformation (Arcsine: arcsin(y/y_max)^0.5), Sokal and Rohlf 1995), or a Hellinger transformation (Hellinger: Legendre and Gallagher 2001). The last two removed the overall intensity of the signal and preserved only the shape information of the sonar returns. STB, BEST, 1–4 m, 4–7 m, and 7–10 m are subtables of ALL, which refers to the complete data set. The STB subtable contained only the echoes acquired while the visibility was optimal and the remotely operated vehicle was in a stable position, hovering at low altitude over the selected habitat. The BEST subtable contained only the best transect for each habitat type. The 1–4 m, 4–7 m, and 7–10 m subtables contained echoes acquired at different altitude ranges, respectively 1 to 4, 4 to 7, and 7 to 10 m.

TABLE A3. Variables retained by forward selection, making the FWD variable sets.

   Notes: The STB, BEST, 1–4, 4–7, and 7–10 subtables are described in the notes of Table A2. Based on their appearance frequencies, the VE variables “DRSx”, “Histo1”, “Skew”, “time.RE1”, “Vmn.s”, “Vmx.sE1”, “Vmx.sE2”, “Newalt” were selected to be included in the SEL variable set. For the VI set, the distribution of the variables selected by forward selection showed that 20% of the variables were describing the rise area of the first echo, and 60% for the set area. Consequently, based on these ratios and on the variable appearance frequencies, “Int11-15”, “Int21-25”, “Int31-35”, “Int46-50”, “Int56-60”, “Int71-75”, “Int91-95”, and “Int181-185” were also selected to be part of set SEL.

LITERATURE CITED

Legendre, P., and E. D. Gallagher. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129:271–280.

Sokal, R. R., and F. J. Rohlf. 1995. Biometry – The principles and practice of statistics in biological research. Third edition. W. H. Freeman, New York, New York, USA.